Keep in mind my husband and I were in GC during the "low season" for tourists, which we were reminded of almost daily when some restaurants and bars were closed, our hotel's bar was closed, and there was no one on the main street most nights past 9pm. It would have been really helpful for us to know the following things, so I hope this helps others who are planning a visit:
There are no ATMs in Grand Case, and even if you charge a restaurant meal, they expect tips in cash, so you need a lot of cash at all times. We didn't feel safe travelling with a lot of $$, but I wish we had just taken the chance because it was a pain driving toward Cul de Sac or Marigot everytime we needed money. The taxi drivers on the French side expect Euro and on the Dutch side they'll tell you they will only take 1 Euro per Dollar (which is a HUGE rip-off), so plan to bring a lot of dollars but also stop at a French ATM to get Euros. You'll use both.
Some of the great restaurants we visited in GC were L'Hibiscus (super-nice owners who talked to us as we were the only people eating the entire time we dined there), Le Cottage (one of the best, most creative meals I've ever had), Le Soleil (pretty good food, nice to be on the deck over the water), Spicy (decent food, laid-back atmosphere), and Calmos Cafe, which was a fun, casual place to have some food or a drink on the sand. It doesn't look like much from the street, but cut down to the beach and you'll find mostly French speaking natives enjoying a cocktail while their kids play in the sand. Very relaxing.
You definitely need to rent a car if you're staying on the French side, as things are pretty far apart. We spent more time in the car each day than I would have liked, but we're city people and not used to driving everywhere. I hear cabs were very expensive from people who relied on them. If you go out at night ask the driver to pick you up at a certain time where he left you. We got stuck at the Princess Casino on our last night because they didn't have taxis on Mondays (?!) and had to pay a random person the casino staff recommended to drive us back to the hotel. Very uncomfortable, but thankfully we got back safely.
As far as crime goes, we didn't have any problems, but we also stayed off the roads after dark, didn't wear jewelry, only brought my camera with me sometimes, carried photocopies, not actual passports (left them in the hotel safe), and when in the water, swam with a dry pack (you can order them online from scuba stores - totally recommend this) which had car and hotel keys, cash, cc cards, etc. I can't say there weren't times we were nervous, as constantly being alone on GC blvd at night and taking some wrong turns off the main road were sketchy, but thankfully nothing happened.
Our day trips were all fun and they were:
Pinel Island (bring lunch since the food there is pricey and not that good)
Orient Beach (grab lunch from the nice deli in the Bikini Beach parking lot)
Anguilla (beautiful country about 25 min by ferry from Marigot - you MUST have your passport and cash for ferry fee[$15 pp each way], taxes on both sides [about $20 pp each way], taxi to Anguilla beaches, lunch, etc)
Maho Beach - not as nice as the other beaches but we wanted to see the Dutch side and watching the first few planes land on top of you is pretty nuts
I wouldn't go to St Martin again, and if I did for some reason, I'd probably stay on the Dutch side because things are closer together, but overall we had a good time, ate great food, and swam at some of the most beautiful beaches imaginable. In general the most important things to bring are lots of cash, a soft cooler to carry lunch and water to the beach, a dry pack so you can swim with valuables, and several bathing suits!